FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Split Gibbs Sampling

Forum topic · 小凯 · 2026-09-19

Summary

FlowSGS is a new flow-based posterior sampling method for inverse problems in computational imaging, proposed by Tianao Li, Xinhui Qian, and Emma Alexander (arXiv 2609.20769). While flow matching has become a state-of-the-art generative model used as a plug-and-play (PnP) prior, existing flow-based inverse solvers typically assume linear forward models or rely on simplifying approximations in posterior sampling. FlowSGS addresses these limitations by applying Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. The likelihood step is sampled via Langevin dynamics, while the prior step integrates a pretrained flow model through the Stochastic Interpolants (SI) framework, formulated with SI's reverse-time SDE and connected to previous PnP methods. Leveraging the straight probability paths of flow priors and a novel time-step correction technique for the reverse SDE, FlowSGS requires fewer network evaluations than PnP diffusion samplers. Experiments across a range of inverse problems show state-of-the-art performance, including the first nonlinear inverse problem (Fourier phase retrieval) experiments for flow-based solvers.

Overview

Field: Computer Vision Authors: Tianao Li, Xinhui Qian, Emma Alexander Published: 2026-09-17 arXiv: 2609.20769

Abstract

Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, the authors introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. Specifically, they sample from the likelihood step using Langevin dynamics and leverage the Stochastic Interpolants (SI) framework to integrate a pretrained flow model into the prior step. They provide a form for the prior step that uses SI's reverse-time SDE, and show connections to previous PnP methods. Additionally, leveraging the straight probability paths of flow priors and a novel time-step correction technique for the reverse SDE, FlowSGS requires fewer network evaluations in the prior step than plug-and-play diffusion samplers. Experiments across a range of inverse problems demonstrate state-of-the-art performance, including the first experiments on a nonlinear inverse problem (Fourier phase retrieval) for flow-based inverse solvers.

Key points

Problem: Existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling.
Method: Split Gibbs Sampling (SGS) decomposes the posterior into a likelihood step (sampled with Langevin dynamics) and a prior step (integrating a pretrained flow model via the Stochastic Interpolants framework).
Formulation: The prior step uses SI's reverse-time SDE, with connections shown to previous PnP methods.
Efficiency: Straight probability paths of flow priors plus a novel time-step correction for the reverse SDE reduce the number of network evaluations compared to PnP diffusion samplers.
Results: State-of-the-art performance across a series of inverse problems, including the first Fourier phase retrieval (nonlinear) experiments for flow-based solvers.

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